Cluster algebras and related topics

Course Description:

This is a graduate level course on
cluster algebras. Cluster algebras are a class of combinatorially
defined rings that provide a unifying structure for phenomena in a
variety of algebraic and geometric contexts. A partial list of
related areas includes quiver representations, statistical physics,
and Teichmuller theory. This course will focus on the algebraic,
geometric and combinatorial aspects of cluster algebras, thereby
providing a concrete introduction to this rapidly-growing field.
Besides providing background on the fundamentals of cluster theory,
we will discuss complementary topics such as total positivity, quiver
representations, the polyhedral geometry of cluster complexes,
cluster algebras from surfaces, and connections to statistical
physics.

Prerequisites: No prior knowledge of cluster
algebras or representation theory will be assumed; although
familiarity with groups, rings, and modules will be helpful.

Grading:

There will be no exams, but registered students are expected to
present (orally) solutions of assigned problems (90% of each section) during office hours.The list of problems will be expanded during the course of the semester. Any form of collaboration on homework between students is welcomed.